Steps to solve everyday problems using the coordinate plane (Grade 6).

📚 Introduction to the Coordinate Plane

The coordinate plane is like a map made of two number lines that cross each other. The horizontal line is called the x-axis, and the vertical line is called the y-axis. Where they cross is called the origin, and it's at point (0, 0).

• 📍 Points: Every point on the coordinate plane has two numbers that tell you where it is. These are called coordinates, and they're written as (x, y). The x number tells you how far to move right or left from the origin, and the y number tells you how far to move up or down.
• 📈 Quadrants: The coordinate plane is divided into four sections called quadrants. We use Roman numerals to label them: I, II, III, and IV. In quadrant I, both x and y are positive. In quadrant II, x is negative and y is positive. In quadrant III, both x and y are negative. In quadrant IV, x is positive and y is negative.

🎯 Objectives

• 🧭 Learn to plot points on the coordinate plane.
• 📐 Understand how the coordinate plane can represent real-world situations.
• 💡 Solve problems using the coordinate plane.

🛠️ Materials

• Graph paper
• Pencils
• Rulers
• Colored pencils or markers (optional)

Warm-up (5 minutes)

Activity: Coordinate Plane Scavenger Hunt

1. Ask students to draw a small coordinate plane on a piece of paper.
2. Call out coordinates (e.g., (2, 3), (-1, 4), (-2, -2), (3, -1)).
3. Have students plot the points as you call them out.
4. Ask students to connect the points in the order you called them out to see what shape they create.

Main Instruction (25 minutes)

🏘️ Example 1: Mapping Your Neighborhood

Imagine you want to map out your neighborhood on a coordinate plane.

• 🏠 Your House: Let’s say your house is at the origin (0, 0).
• 🌳 The Park: The park is 3 blocks east and 2 blocks north of your house. That means the park is at point (3, 2).
• 🏫 The School: The school is 4 blocks west and 1 block north of your house. That means the school is at point (-4, 1).
• 🛍️ The Store: The store is 2 blocks east and 3 blocks south of your house. That means the store is at point (2, -3).

Now, you can plot these points on a coordinate plane to create a map of your neighborhood!

🚶 Example 2: Planning a Walk

You want to plan a walk from your house to the park and then to the store.

• 🗺️ Step 1: Plot your house (0, 0), the park (3, 2), and the store (2, -3) on the coordinate plane.
• 📏 Step 2: Draw a line from your house to the park and then from the park to the store.
• 🧭 Step 3: Use the coordinate plane to estimate how far you will walk. For example, from (0,0) to (3,2) is roughly 3 blocks east and 2 blocks north. From (3,2) to (2,-3) is roughly 1 block west and 5 blocks south.

📦 Example 3: Organizing Your Room

Let's say you want to organize your room and use a coordinate plane to plan where to put things.

• 🧸 Toys: Your toy box is at (1, 2).
• 📚 Books: Your bookshelf is at (-2, 3).
• 🛏️ Bed: Your bed is at (-3, -2).
• Desk: Your desk is at (2,-1).

You can use these coordinates to draw a map of your room and decide if you want to rearrange anything!

📝 Assessment (15 minutes)

Activity: Problem-Solving on the Coordinate Plane

1. Provide students with a worksheet that includes several scenarios that require them to use the coordinate plane to solve problems. Examples:
2. Problem 1: A treasure is buried at the point (4, -2) on a map. Write instructions on how to find the treasure starting from the origin (0,0).
3. Problem 2: Maria walks from (1, 1) to (5, 3). How many blocks east and north did she walk?
4. Problem 3: A new park is being built. The entrance is at (-2, 0), and a playground will be at (3, 4). How far apart are the entrance and the playground (in terms of blocks east/west and north/south)?

🔑 Answer Key (For Teacher Use)

• 🗺️ Problem 1: The treasure is 4 blocks east and 2 blocks south of the origin.
• 🚶 Problem 2: Maria walked 4 blocks east and 2 blocks north.
• 🏞️ Problem 3: The playground is 5 blocks east and 4 blocks north of the entrance.